Tool to generate permutations of items, the arrangement of distinct items in all possible orders: 123,132,213,231,312,321.

Permutations - dCode

Tag(s) : Combinatorics

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In Mathematics, item permutations consist in the list of all possible arrangements (and ordering) of these elements in any order.

__Example:__ The three letters `A,B,C` can be shuffled (anagrams) in 6 ways: `A,B,C` `B,A,C` `C,A,B` `A,C,B` `B,C,A` `C,B,A`

Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Here is a pseudo code source : `function permute(data, n) {`

if (n = 1) print data

else {

for (i = 0 .. n-2) {

permute(data, n-1)

if (n % 2) swap(data[0], data[n-1])

else swap(data[i], data[n-1])

permute(data, n-1)

}

}

}

Permutations can thus be represented as a tree of permutations:

Counting permutations uses combinatorics and factorials

__Example:__ For $ n $ items, the number of permutations is equal to $ n! $ (factorial of $ n $)

Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.

__Example:__ `DCODE` 5 letters have $ 5! = 120 $ permutations but contain the letter `D` twice (these $ 2 $ letters `D` have $ 2! $ permutations), so divide the total number of permutations $ 5! $ by $ 2! $: $ 5!/2!=60 $ distinct permutations.

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Cite as source (bibliography):

*Permutations* on dCode.fr [online website], retrieved on 2024-07-15,

permutation,arrangement,order,anagram,combinatorics,distinguishable

https://www.dcode.fr/permutations-generator

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